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### Overview

This course provides a series of math topics for students to select from based on their needs. It can be used for math acceleration, remediation or to supplement existing curriculum. Each topic begins with a pre-assessment from which a personal learning path is developed for the student. Based on the pre-assessment, the learning path includes refreshers on concepts students may have forgotten and lessons on concepts the student has not yet mastered. The learning path does not require students to complete lessons on concepts the student has mastered.

### Course Requirements

Students work with a certified VLACS math teacher throughout the course. The teacher coaches the student through the course by completing a Welcome Call at the beginning of the course, monitoring student progress, identifying areas of struggle, meeting regularly with the student, and completing monthly calls with the student and parent.

Students may work with their school to identify the set of topics that meet their needs. The groupings below are provided to aid in potential sets of topics, but students may select whatever topics meet their particular needs.

Credit for completion of topics will be determined by the student’s school of record. VLACS will not award credit, but will report topics in which a student has demonstrated competency, which can be used by schools to award credit. Credit Recommendations: VLACS recommends that students be awarded 0.5 credits for each set of 4 competencies completed.

### Major Topics and Concepts

Pre-Algebra Competencies:

• Whole numbers
• Fractions and Mixed Numbers
• Decimals
• Ratios, Rates, and Proportions
• Percents
• Measurements

Geometry Competencies:

• Figures in 1 and 2 Dimensions
• Properties of Angles
• Triangles
• The Pythagorean Theorem
• Perimeter and Area
• Circles
• Solids

Statistics Competencies:

• Graphing Data
• Other Types of Graphs
• Measures of Center
• Use and Misuse of Graphical Representations
• Probability

Algebra 1 Competencies:

• Real Numbers
• Solving Equations and Inequalities
• Exponents and Polynomials
• Factoring
• Graphing
• Systems of Equations and Inequalities

• Rational Expressions
• Functions
• Exponential and Logarithmic Functions

Trigonometry Competencies:

• Introduction to the Trig Functions
• Graphing Trig Functions

### Competencies

• Adv. Algebra: Exponential and Logarithmic Functions
Students will demonstrate an understanding of exponential and logarithmic functions by converting between the two forms; using properties to simplify and solve logarithmic and exponential functions; graphing and solving logarithmic and exponential equations with various bases including "e"; and solving applied problems using both types of functions.
Students will demonstrate an understanding of functions by identifying whether a relation is a function by multiple means; evaluating and graphing linear, quadratic and radical functions; identifying domain and range of functions; and performing operations with two or more functions.
Students will demonstrate understanding of radical expressions by finding and approximating square and cubic roots; simplifying expressions with odd and even roots; converting between radicals and exponential notation; simplifying radical expressions; performing operations with radical expressions; rationalizing denominators; solving radical equations; performing operations with complex numbers; solving quadratics by completing the square; and solving application problems requiring the quadratic formula and having complex solutions.
Students will demonstrate an understanding of rational expressions by simplifying and performing operations with rational expressions; solving problems involving rational expressions; simplifying complex rational expressions; identifying extraneous solutions; and solving problems involving direct, inverse and joint variations.
• Algebra: Exponents and Polynomials
Students will demonstrate an understanding of exponents by solving problems with integer exponents; simplifying exponential expressions using properties of exponents; and working with scientific notation. Students will also demonstrate an understanding of polynomials by using polynomial terminology; simplifying and evaluating polynomials; performing operations involving multiple polynomials with one or multiple variables; and evaluating polynomials.
• Algebra: Factoring
Students will demonstrate an understanding of factoring by factoring polynomials using greatest common factors and grouping; factoring trinomials of all types; factoring special case cubics using sum and difference formulas; and solving equations using factoring and the quadratic formula.
• Algebra: Graphing Linear Equations and Inequalities
Students will demonstrate an understanding of graphing linear equations and inequalities by finding the slop of a line graphically and through calculations; writing the equation of a line given various types of information; determining if lines are parallel and perpendicular based on slopes; and graphing linear equations and inequalities.
• Algebra: Real Numbers
Students will demonstrate an understanding of real numbers by evaluating expressions with multiple variables; defining, performing operations and solving problems with integers; defining, performing operations and solving problems with real numbers; identifying irrational numbers; identifying and using the commutative, associative and distributive properties; and solving problems using order of operations.
• Algebra: Solving Equations and Inequalities
Students will demonstrate an understanding of how to work with equations and inequalities by solving one and multi-step equations; solving equations that have one solution, no solution or an infinite number of solutions; evaluating and manipulating formulas; solving one and multi-step inequalities; solving compound inequalities; and solving equations and inequalities involving absolute values.
• Algebra: Systems of Equations and Inequalities
Students will demonstrate an understanding of systems of equations and inequalities by solving systems of equations and inequalities graphically and through calculations (substitution an elimination); solving problems involving systems of both equalities and inequalities; and solving systems of equations involving three variables by calculation.
• Geometry Concepts
Students will demonstrate an understanding of various geometry concepts including figures in 1 and 2 dimensions; properties of angles; types and properties of triangles; pythagorean theorem; types and properties of quadrilaterals; perimeter and area of polygons; properties, area and circumference of circles; and problem solving with solids.
• Pre-Algebra: Decimals
Students will demonstrate an understanding of decimals and fractions by reading and writing numbers in decimal notation, converting between decimals and fractions, ordering and rounding decimals, performing operations with decimals (+, -, x, /), and estimating the solution to problems involving decimals.
• Pre-Algebra: Fractions and Mixed Numbers
Students will demonstrate an understanding of fractions and mixed numbers by identifying parts of a fraction, converting between proper and improper fractions, simplifying, comparing, and performing operations with fractions and mixed numbers.
• Pre-Algebra: Measurement
Students will demonstrate understanding of various forms of measurements by defining units of measurement and converting between various units for length, weight and capacity, converting between celsius and fahrenheit, describing the relationships between the US customary units and the corresponding metric units, and working with various metric units of measurements to solve problems.
• Pre-Algebra: Percents
Students will demonstrate an understanding of percents by describing the meaning of percents, converting between percents, decimals and fractions, and solving problems involving percents.
• Pre-Algebra: Ratios, Rates and Proportions
Students will demonstrate an understanding of rations, rates and proportions by simplifying ratios and rates, finding unit rates and prices, evaluating the validity of proportions and solving problems using proportions.
• Pre-Algebra: Whole Numbers
Students will demonstrate an understanding of whole numbers by naming, rounding, comparing, performing operations, utilizing properties and laws, evaluating exponents and square roots, and using order of operations to solve problems.
• Statistics Concepts
Students will demonstrate an understanding of statistical concepts including various forms in which data can be represented graphically; measures of central tendency; misuses of graphical representation; and basic probability concepts, terminology and problem solving.
• Trigonometry
Students will demonstrate an understanding of trigonometry concepts by using the six trigonometric ratios to solve problems; solving right triangle application problems using the Pythagorean Theorem and special right triangles; working with the unit circle as it relates to the six trigonometric functions; completing calculations with both radians and degrees; graphing the sine and cosine functions; and adjusting the graphs of sine and cosine by manipulating the amplitude and/or period.

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## Attend a virtual open house

We offer regular online open house webinars where VLACS staff members provide parents and students with an overview of our programs and answer questions about online learning.